There is a light sensor on your dashboard. When it gets dark enough, because it's dusk, or your drive into a tunnel, or there's a solar eclipse, it will automatically turn on the headlights (and taillights), if the switch is set to auto. When you drive out of the tunnel or the eclipse is over, the lights will turn off. Do you have a lot of stuff piled on the dashboard of your car? Maybe you have an electrical problem. When you checked the taillights, did you have the parking brake engaged?

Often times, when it rains, it's also dark enough to trigger the automatic headlights. But not always. Some cars turn on the headlights (and tailights) when the wipers are on, if the switch is set to auto. Yours may not.